{"paper":{"title":"On the two-copy distillability of Werner states and a new partial trace inequality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"quant-ph","authors_text":"Bal\\'azs Pozsgay, Felix Huber, Istv\\'an Vona, Thomas C. Fraser","submitted_at":"2026-07-27T11:51:18Z","abstract_excerpt":"Problem 5 in {\\it Five Open Problems in Quantum Information Theory} [PRX Quantum 3, 010101 (2022)], asks whether the two-ququart Werner state $\\varrho(4,-\\tfrac12)$ is two-copy distillable, where $\\varrho(d,\\alpha)=(I+\\alpha F)/(d^2+\\alpha d)$. We answer it in the negative. To this end, we show the following stronger statement: for all $C\\in M_{d_1d_2}(\\mathbb{C})$ of rank at most $r \\le d_1 d_2$, $\\mathrm{tr}_1(C)\\|_F^2+\\|\\mathrm{tr}_2(C)\\|_F^2 \\le r\\|C\\|_F^2+\\frac{1}{r}|\\mathrm{tr}(C)|^2$. A result by Costa Rico on the equivalence of this inequality with two-copy undistillability at $r = 2$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24309","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.24309/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}